1. Field of the Invention
The present invention relates to reconstruction in cone beam computed tomography (CT), and in particular to generating approximations to missing data in circular scan cone beam CT.
2. Discussion of the Background
In volume CT, or cone-beam CT, the x-ray scanner employs multi-row detector arrays and x-ray beam collimation that results in a cone-like shape of the x-ray beam, illuminating the whole area-detector. These two features coupled with ultra fast (such as 0.5 sec/rotation) rotation of the x-ray tube along a circular trajectory, provide the volume CT scanner with the capability to acquire large amounts of data in a very short time. The weakest point of volume CT is the lack of an adequate reconstruction method. The most common reconstruction method used in volume CT is the Feldkamp reconstruction (also known as cone-beam reconstruction). However when the scan geometry is such that large cone angles are involved, Feldkamp images suffer from serious artifacts. The reason for these artifacts is that the circle data is not a complete data set in the sense of 3-D tomography. The data set which is necessary to complement the circular data set into a complete data set is called the missing data.
Many attempts were made to improve the Feldkamp reconstruction based on ad hoc methods, but no robust solution was achieved. Although it was considered by it""s inventors as an approximate cone beam reconstruction method, the Feldkamp reconstruction was shown later to be an exact method when the scan data is collected only along a circular trajectory. The problem is not the reconstruction algorithm but the fact that the data collected along a circular trajectory is incomplete. The missing data issue was first recognized by Grangeat who considered the circle trajectory scan from a fully 3D point of view.
Grangeat""s theorem relates the processed cone beam x-ray transform (data collected by cone beam scanners) to the first derivative (with respect to the signed distance from the origin) of the 3D Radon transform. The 3D Radon transform is defined on planes, and therefore he considered the locus of all the vectors perpendicular to those planes for which the 3D Radon transform is required. He coined the name Shadow Zone given to the group of vectors for which the Radon transform on the corresponding planes can not be obtained by the circle scan. Using this graphical description Grangeat also proposed to obtain approximations of the data corresponding to the vectors in the Shadow Zone (missing data) by interpolation of the known data belonging to vectors on the border of the Shadow Zone. Grangeat proposed methods to approximate the missing data, but his methods of counting the planes, obtaining the approximations, and finally reconstructing all the data, are all very complicated and time consuming.
One way to solve the missing data issue is to use different scan geometry by performing the volume scan along a different trajectory. In the orthogonal line and circle scan, the data collected along the line complements the data collected along the circular trajectory into a complete data set. However, the addition of the linear motion of the couch results in the loss of the speed advantage of the volume scanner and subjects the patient to a much longer time in the scanner and to a higher radiation dose.
It is an object of the present invention to reconstruct images using approximated missing data.
It is a further object of the invention to approximate missing data and to reconstruct it, thereby improving the image quality of reconstructed images.
It is still further object of the invention to generate virtual line data that can complete circular data, improving reconstruction of images.
According to the invention, in approximating the missing data, data may be collected along a circular trajectory complemented by the data that could be collected along a line trajectory is a complete data set. The data that could be collected along the line trajectory is approximated, and used in the reconstruction of images.
These and other objects of the invention may be obtained by the method according to the invention where an image is reconstructed by scanning a stationary object along a circular trajectory to obtain projection data. Circle data is reconstructed from the projection data, and line data is approximated using the circle data. The image is reconstructed using the circle data and the approximated line data.
The circle data may be processed by weighting, integrating, differentiating and then dividing by co-inclination factor. The line data may be generated using the processed circle data.
The line data may be generated using edge planes. The edge planes pass through a line from a particular focal spot position to a detector cell and touch the scan circle at one point. Data related to the edge planes can be obtained from data collected along the scan circle.
Approximating the line data may comprise generating line data that will complete a circular data set corresponding to the circle data.
The circle data may be reconstructed using a Feldkamp reconstruction technique and the image may be reconstructed using a method based upon a Kudo and Saito algorithm.
The method according to the invention may also comprise scanning a stationary object along a circular trajectory to obtain image data, reconstructing circle data from the image data, approximating line data using the circle data and correcting the circle data using approximated line data.
The present invention is also directed to a computed tomography apparatus having an x-ray source for exposing an object to a cone beam of x-rays, and an x-ray detector arranged to receive the beam of x-rays. In one embodiment, a first reconstruction processor is connected to the data acquisition device to reconstruct a circle view from the projection data, a missing data calculator is connected to the data acquisition device to calculate data missing from the circle view, a line data processor is connected to the missing data calculator, a second reconstruction processor is connected to the line data processor, and an image addition processor is connected to the first and second reconstruction processors.